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<div class="subTitle">org.apache.commons.math3.analysis.integration.gauss</div>
<h2 title="Class HermiteRuleFactory" class="title">Class HermiteRuleFactory</h2>
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<li><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html" title="class in org.apache.commons.math3.analysis.integration.gauss">org.apache.commons.math3.analysis.integration.gauss.BaseRuleFactory</a>&lt;<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>&gt;</li>
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<li>org.apache.commons.math3.analysis.integration.gauss.HermiteRuleFactory</li>
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<pre>public class <span class="strong">HermiteRuleFactory</span>
extends <a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html" title="class in org.apache.commons.math3.analysis.integration.gauss">BaseRuleFactory</a>&lt;<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>&gt;</pre>
<div class="block">Factory that creates a
 <a href="http://en.wikipedia.org/wiki/Gauss-Hermite_quadrature">
 Gauss-type quadrature rule using Hermite polynomials</a>
 of the first kind.
 Such a quadrature rule allows the calculation of improper integrals
 of a function
 <p>
  \(f(x) e^{-x^2}\)
 </p><p>
 Recurrence relation and weights computation follow
 <a href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun">
 Abramowitz and Stegun, 1964</a>.
 </p><p>
 The coefficients of the standard Hermite polynomials grow very rapidly.
 In order to avoid overflows, each Hermite polynomial is normalized with
 respect to the underlying scalar product.
 The initial interval for the application of the bisection method is
 based on the roots of the previous Hermite polynomial (interlacing).
 Upper and lower bounds of these roots are provided by </p>
 <blockquote>
  I. Krasikov,
  <em>Nonnegative quadratic forms and bounds on orthogonal polynomials</em>,
  Journal of Approximation theory <b>111</b>, 31-49
 </blockquote></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.3</dd></dl>
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<td class="colOne"><code><strong><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/HermiteRuleFactory.html#HermiteRuleFactory()">HermiteRuleFactory</a></strong>()</code>&nbsp;</td>
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<td class="colFirst"><code>protected <a href="../../../../../../../org/apache/commons/math3/util/Pair.html" title="class in org.apache.commons.math3.util">Pair</a>&lt;<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>[],<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>[]&gt;</code></td>
<td class="colLast"><code><strong><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/HermiteRuleFactory.html#computeRule(int)">computeRule</a></strong>(int&nbsp;numberOfPoints)</code>
<div class="block">Computes the rule for the given order.</div>
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<code><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html#addRule(org.apache.commons.math3.util.Pair)">addRule</a>, <a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html#getRule(int)">getRule</a>, <a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html#getRuleInternal(int)">getRuleInternal</a></code></li>
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<h4>HermiteRuleFactory</h4>
<pre>public&nbsp;HermiteRuleFactory()</pre>
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<h4>computeRule</h4>
<pre>protected&nbsp;<a href="../../../../../../../org/apache/commons/math3/util/Pair.html" title="class in org.apache.commons.math3.util">Pair</a>&lt;<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>[],<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>[]&gt;&nbsp;computeRule(int&nbsp;numberOfPoints)
                                       throws <a href="../../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre>
<div class="block">Computes the rule for the given order.</div>
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<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html#computeRule(int)">computeRule</a></code>&nbsp;in class&nbsp;<code><a href="../../../../../../../org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.html" title="class in org.apache.commons.math3.analysis.integration.gauss">BaseRuleFactory</a>&lt;<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Double.html?is-external=true" title="class or interface in java.lang">Double</a>&gt;</code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>numberOfPoints</code> - Order of the rule to be computed.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the computed rule.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the elements of the pair do not
 have the same length.</dd></dl>
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